By 26 million years ago, the ancestors of today’s New World monkeys had arrived in South America. How those primates reached the continent is something of a conundrum. The leading explanation has the animals floating across the Atlantic Ocean from Africa aboard a giant raft of vegetation.

The scenario may sound preposterous. But de Queiroz, an evolutionary biologist, uses fossil, genetic and geologic evidence to make a compelling case that a variety of plants and animals have dispersed on long...